Method for performing joint jitter and amplitude noise analysis on a real time oscilloscope

ABSTRACT

A method for determining jitter and noise of an input signal. The method includes acquiring one or more uncorrelated waveform records by an acquisition unit of a test and measurement instrument, determining a correlated waveform from the acquired waveform(s), dividing the correlated waveform into unit intervals, dividing an uncorrelated waveform into unit intervals, measuring a timing displacement (t 1 ) between the correlated waveform and the uncorrelated waveform for each unit interval to form an apparent-jitter array ([t 1 ]), measuring a voltage displacement (V 1 ) between the correlated waveform and the uncorrelated waveform for reach unit interval to form an apparent-noise array ([V 1 ]), calculating a horizontal shift (t s ) between the correlated waveform and the uncorrelated waveform for each unit interval to form a compensated edge time array ([t s ]), and calculating a vertical shift (V s ) between the correlated waveform and the uncorrelated waveform for each unit interval to form a compensated amplitude voltage array ([V s ]).

PRIORITY

This application claims benefit of U.S. Provisional Application No.62/031,069 filed Jul. 30, 2014, which is hereby incorporated byreference in its entirety.

TECHNICAL FIELD

This disclosure relates to performing joint jitter and amplitude noiseanalysis to generate two-dimensional probability density functions andbit error rate eye diagrams.

BACKGROUND

In the field of high-speed serial data communication, analysis of timingjitter has been of interest. Many concepts were formalized with apublication of the Fibre Channel Methodologies for Jitter and SignalQuality Specification (Technical Report TR-35-2004, Washington, D.C.:ANSI/INCITS, 2004). The methods described in the Fibre ChannelMethodologies for Jitter and Signal Quality Specification allow analysisof timing jitter at a specific reference voltage. The reference voltagecorresponds to a horizontal slice through an eye diagram at the givenlevel. However, the methods make no attempt to analyze voltage noise.

U.S. Pat. No. 7,522,661, titled “METHOD OF PRODUCING A TWO-DIMENSIONALPROBABILITY DENSITY FUNCTION (PDF) EYE DIAGRAM AND BIT ERROR RATE EYEARRAYS,” incorporated herein by reference in its entirety, describes amethod of first performing a voltage analysis on a waveform locationthat is flat (i.e., has zero slew rate) and is therefore theoreticallyunaffected by timing jitter. Then, a jitter analysis is performed on ahigh-slew-rate area in which the effects of noise are mathematicallyremoved. Together, with additional steps described in U.S. Pat. No.7,522,661, a statistical description of the eye at all points verticallyand horizontally can be determined.

Sampling oscilloscopes are well known. When utilized to measurerepeating high frequency electrical waveforms, such devicesconventionally sample small sequential portions of successive waveforms.Thus, the cumulative result of this sampling technique provides acomposite waveform readout representative of the subject waveforms. Themethod described in U.S. Pat. No. 7,522,661 is well-adapted to thestrengths of a sampling oscilloscope, which can be configured torepetitively sample and store a particular location in a repeatingwaveform without wasting memory or other resources on the remainder ofthe waveform. The method of U.S. Pat. No. 7,522,661 gathers informationto separate jitter from noise using only two sampling locations perpattern repetition.

In contrast, a real-time digitizing oscilloscope acquires and storessamples spaced closely-enough that the features of the waveform can berepresented directly by the sequential samples. The method of U.S. Pat.No. 7,522,661 results in low efficiency on a real-time oscilloscopesince most of the acquired samples are thrown out without being used.This lack of efficiency becomes more pronounced as pattern lengthincreases. To accumulate sufficient statistics on sampling locationschosen as described in U.S. Pat. No. 7,522,661, a real-time oscilloscopehas to acquire and process many real-time waveforms. In addition, thereal-time oscilloscope possesses valuable information about the dynamiccharacteristics of the waveform in the vicinity of a target analysispoint, such as the slope of the preceding edge, but the method of U.S.Pat. No. 7,522,661 fails to take advantage of this information.

Embodiments of the invention address these and other limitations in theprior art.

SUMMARY

According to aspects illustrated herein, there is provided a method fordetermining jitter and noise of an input signal. The method includesacquiring one or more uncorrelated waveform records by an acquisitionunit of a test and measurement instrument, determining a correlatedwaveform from the acquired waveform(s), dividing the correlated waveforminto unit intervals, dividing the at least one uncorrelated waveforminto unit intervals, measuring a timing displacement (t₁) between thecorrelated waveform and the uncorrelated waveform for each unit intervalto form an apparent-jitter array ([t₁]), measuring a voltagedisplacement (V₁) between the correlated waveform and the uncorrelatedwaveform for each unit interval to form an apparent-noise array ([V₁]),calculating a horizontal shift (t_(s)) between the correlated waveformand the uncorrelated waveform for each unit interval to form acompensated edge time array ([t_(s)]), and calculating a vertical shift(V_(s)) between the correlated waveform and the uncorrelated waveformfor each unit interval to form a compensated amplitude voltage array([V_(s)]).

According to other aspects illustrated herein, there is provided a testand measurement instrument. The test and measurement instrument includesacquisition means configured to receive one or more uncorrelatedwaveform records and processing means. The processing means determines acorrelated waveform, divides the correlated waveform into unitintervals, divides the at least one uncorrelated waveform into unitintervals, measures a timing displacement (t₁) between the correlatedwaveform and the uncorrelated waveform for each unit interval to form anapparent-jitter array ([t₁]), measures a voltage displacement (V₁)between the correlated waveform and the uncorrelated waveform for reachunit interval to form an apparent-noise array ([V₁]), calculates ahorizontal shift (t_(s)) between the correlated waveform and theuncorrelated waveform for each unit interval to form a compensated edgetime array ([t_(s)]), and calculates a vertical shift (V_(s)) betweenthe correlated waveform and the uncorrelated waveform for each unitinterval to form a compensated amplitude voltage array ([V_(s)]).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a block diagram of a test and measurement instrumentfor implementing the method for performing joint jitter and noiseanalysis.

FIG. 2 illustrates an idealized serial data waveform.

FIG. 3 illustrates a waveform with impairments and defines a unitinterval.

FIGS. 4-6 illustrate superimposed unit intervals of a correlatedwaveform and an uncorrelated waveform.

FIGS. 7 and 8 illustrate waveforms with more complex patterns andimpairments.

DETAILED DESCRIPTION

In the drawings, which are not necessarily to scale, like orcorresponding elements of the disclosed systems and methods are denotedby the same reference numerals.

The disclosed technology uses information from a vertical displacementin the center of every bit and a horizontal displacement on every edgeto give a very high processing efficiency that is well-matched with thecharacteristics of a real-time oscilloscope. That is, the method of thedisclosed technology uses all unit intervals in a pattern and does notrely only on measurement locations with a zero slew rate.

Referring now to FIG. 1, there is shown a representative block diagramof a real-time oscilloscope according to some embodiment of the presentinvention for implementing the method of performing joint jitter andnoise analysis. Although a real-time oscilloscope is shown and discussedbelow, any type of test and measurement instrument capable of acquiringa suitable representation of a time-domain waveform may be used.

The oscilloscope 100 may have separate signal channels 102 coupled toaccessory interfaces 104, two of which are represented in FIG. 1. Eachsignal channel 102 may have a separate acquisition unit 106 that mayinclude, for example, known electronic circuitry and/or devices for atleast receiving an analog waveform input signal from the a device undertest or channel and converting the received signal into digitizedsamples. Each of the analog waveform input signals coupled to the signalchannels 102 may also be coupled to trigger circuitry 108. Theacquisition unit 106 and the trigger circuitry 108 may be coupled to aprogrammable processing means 110 via a system bus 112. The system bus112 may be further coupled to memory means 114 that may, for example,take the form of RAM, ROM and/or cache memory. RAM memory is operable tostore volatile data, such as the digitized samples of the analogwaveform input signal generated by the acquisition unit 106. The systembus 112 may be further coupled to display circuitry 116 for controllinga display section (not shown), a mass storage unit or units 118, such asa hard disk drive, CD ROM drive, tape drive, floppy drive or the likethat reads from and/or writes to appropriate mass storage media, and thefront panel controls 120. It should be understood that any number ofsignal channels 102 may be included in the oscilloscope 100 with eachchannel having separate acquisitions means 106.

Executable instructions for implementing the methods according toembodiments of the disclosed technology and for otherwise controllingthe oscilloscope 100 may be stored and accessed from memory means 114,more particularly, for example from ROM. Alternatively, the executableinstructions may be stored and accessed from mass storage media of themass storage unit 118 which in some embodiments may be included withinmemory means 114. The processing means 110 may be implemented as, forexample, one or more programmable microprocessors, such as thosedesigned and developed by Intel Corporation. The processing means 110may also be implemented using multiple programmable controllers and/orone or more programmable digital signal processors. In yet anotherembodiment, when the processing means 110 is implemented using multiplecontrollers one may be used to control the acquisition and processing ofthe analog waveform input signal while the second may control the otheroperations of the oscilloscope 100. The oscilloscope 100 may becontrolled using an operating system, such as Windows® 7, designed anddeveloped by Microsoft, Corporation that is stored and accessed withinone or more processors or controllers 110 and associated memory means100.

The display circuitry 116 may include a display controller (not shown)for receiving instructions for controlling the display section fromprocessing means 110 and may receive data as well from a digital signalprocessor, for example, that is a part of processing means 110 fordisplay by the display section. A bus controller (not shown) may also beincluded within the processing means 110 or included separately withinthe oscilloscope 100 for monitoring interfaces 104 and probes 122. Thebus controller may also control communications between the probes 122and the processing means 110 via communications bus 124. The bus 124 maycomprise an I²C bus, IEEE 1494 bus, USB bus or the like, that providesbi-directional communications.

A power supply 126 may receive control signals from the processing means110 for controlling the electrical power to the probes 122 via voltagelines 128 and the accessory interfaces 104.

FIG. 2 depicts an idealized serial data waveform 200 representing analternating bit pattern ‘1 0 1 0 1 0’. However, real waveforms do nothave edges with infinite slew rates, and seldom have perfectly flat topsand bottoms. So a more realistic waveform 300 that uses a simplisticpiecewise-linear model for each edge and flat spot is shown in FIG. 3.

Area A in FIG. 3 shows one unit interval (UI) of the waveform. Thedisclosed technology determines how the actual values in each repeat ofthis uncorrelated waveform pattern deviate from the correlated waveform,which is the deterministic component of the waveform. The correlatedwaveform is the actual data pattern in the input signal and theuncorrelated waveform is the horizontal jitter and vertical noise in theinput signal and the oscilloscope 100. That is, the uncorrelatedwaveform is the waveform real-time oscilloscopes naturally acquire. Oneor more uncorrelated waveform is acquired by the acquisition unit 106 ofthe oscilloscope 100.

The correlated waveform is then determined via the processing means 110based on the one or more uncorrelated waveforms acquired by thereal-time oscilloscope using any known methods. This may be done, forexample, by acquiring multiple uncorrelated waveforms, using apattern-based trigger, and averaging them together. Further, thecorrelated waveform may be determined using a single long uncorrelatedwaveform record, for example by averaging together successive copies ofthe repeating part of the waveform, after suitable time alignment of theindividual copies. The uncorrelated waveform acquired may have arepeating pattern. For example, the uncorrelated waveform may contain arepeating pattern with a length of 9 bits. The correlated waveform maybe determined for the repeating pattern, and then repeated end-to-end tocreate the entire correlated waveform to be compared with the entireuncorrelated waveform record.

FIG. 4 shows one unit interval of a correlated waveform 400 and theuncorrelated waveform 402, using the same piece-wise linear model asdiscussed above. The horizontal and vertical displacement between thecorrelated waveform 400 and the uncorrelated waveform 402 is a measureof the uncorrelated jitter and noise. Time displacements to the rightmay be designated as positive time shifts and voltage shifts upward maybe designated as positive voltage shifts, although other conventions maybe used as long as they are consistently applied.

In FIG. 4, the waveform 402 is not subject to any timing jitter, and isdisplaced upward by a constant voltage noise, shown as V_(s). Inreality, noise isn't constant across a UI, but noise of a sufficientlylow frequency relative to the bit rate can be regarded as constant as areasonable approximation. SR_(V) designates the slew rate of thewaveform 402 on the nominally vertical portion. SR_(H) designates theslew rate on the nominally horizontal portion.

Even though there is no timing jitter in FIG. 4, there is an apparentjitter since the point at which the rising edge crosses a referencevoltage (V_(ref)) has changed. The apparent timing displacement can beseen to be −t₁. The apparent voltage displacement is determined at anominal timing point, shown as t_(ref), normally at the center of thebit. The apparent voltage displacement is shown as V₁ in FIG. 4. Thefollowing equations can be written based on the observations of FIG. 4:

V ₁ =V _(s)  (1)

t ₁ =−V _(s) /SR _(V)  (2)

The negative sign in equation (2) is due to the upward voltage shiftcausing an apparent timing shift to the left.

FIG. 5 shows a unit interval of a correlated waveform 500 and anuncorrelated waveform 502. In FIG. 5, the displacement is caused by apurely horizontal shift, t_(s), and the corresponding equations can bewritten, as follows.

V ₁ =−SR _(H) *t _(s)  (3)

t ₁ =t _(s)  (4)

The negative sign in equation (3) shows that a rightward timing shiftresults in an apparent voltage shift downward, if SR_(H) is positive.

FIG. 6 shows a unit interval of a correlated waveform 600 and anuncorrelated waveform 602. In FIG. 6, the uncorrelated waveform 602 hasbeen displaced both vertically and horizontally for this unit interval.By superposition, equations (1) and (3) can be combined to obtainequation (5), below, and equations (2) and (4) can be combined to obtainequation (6), below. This leaves two unknowns in each of the equations,t_(s) and V_(s).

V ₁ =V _(s) −SR _(H) *t _(s)  (5)

t ₁ =t _(s)−(1/SR _(V))*V _(s)  (6)

Equations (5) and (6) express the apparent, or directly measurable,waveform displacement in terms of the true vertical and horizontalshift. Equations (5) and (6) may be algebraically manipulated to lead tothe following equations, which allow the true shifts to be calculatedfrom the measured displacements:

t _(s)=(V ₁ +SR _(V) *t ₁)/(SR _(V) −SR _(H))  (7)

V _(s) =V ₁ +SR _(H) *t _(s)  (8)

Equations (7) and (8) can be applied for each unit interval in thewaveform record so that the directly measureable t₁ and V₁ are jointlyconverted to t_(s) and V_(s) for that interval. For a waveformconsisting of N unit intervals, or bits, this results in two numericalarrays: The compensated edge time array t_(s)=[t_(s1), t_(s2), t_(s3), .. . t_(sN)] and the compensated amplitude array V_(s)=[V_(s1), V_(s2),V_(s3), . . . V_(sN)]. These arrays can be processed in various ways inorder to derive further information about jitter and voltage noisebehavior, and to allow a statistical eye diagram to be formed, asdiscussed in more detail below.

To apply equations (7) and (8) to real signals rather than to thepiece-wise linear model that was assumed for their development, theparameters t₁, V₁, SR_(V) and SR_(H) must be determined for each unitinterval. It is straightforward to determine t₁ by computing the pointsat the two ends of the t₁ vector and performing a subtraction. Thesubtracted endpoint may be determined by any of the well-knowninterpolation methods, such as linear or sin (x)/x, using nearby actualwaveform samples from the correlated or uncorrelated waveforms. Thesimplest way to determine SR_(V) is to locate the sample of thecorrelated waveform that most closely precedes the point where thecorrelated waveform crosses V_(ref), and compute the slew rate betweenthis sample and the subsequent sample as the voltage difference dividedby the time difference. Similarly, SR_(H) can be computed from the twosamples of the correlated waveform that precede and follow t_(ref).Other slew rate estimation means can easily be devised (for example byusing more than just the two closest samples) to provide SR_(V) andSR_(H) values representative of a wider section of the waveform.

The above equations (1)-(8) perform quite well for small-signal analysisof an alternating-bit pattern. However, these equations can be modifiedto make the usefulness of the equations more general.

In many cases, as seen in FIG. 7, a waveform to be analyzed may carry amore complex pattern than alternating 1's and 0's. FIG. 7 shows a onerepeat of a nine-bit pattern. In FIG. 7, the logical values (1 or 0)corresponding to each interval are shown in the centers of theintervals, and the bit numbers that unique identify each bit in thepattern are shown as subscripted ‘B’s. The nine-bit pattern isunderstood to repeat indefinitely, and the waveform in FIG. 7 representsa correlated waveform for a single repeat of the waveform.

Compare to the waveform shown in FIG. 3, it can be seen that some bitsin FIG. 7, such as B₁, can be modeled in an analogous way, using alinearizes SR_(V) for the voltage transition and an SR_(H) for thecenter of the bit interval. Similar values can be determined for bitsB₃, B₄, B₅, B₈, and B₉. These bits are called transition bits. But fornon-transition bits, that is, those that follow another bit of the samelogical value, such as B₂, B₆, and B₇, there is no vertical transitionat the beginning of the bit and therefore no corresponding SR_(V).

The voltage deviation from the correlated waveform (V₁) can be measuredfor each unit interval, but the timing deviation (t₁) can only bemeasured when there is an edge. Therefore, equations (7) and (8)discussed above cannot be directly applied to determine the compensatededge time array or the compensated amplitude array.

To solve this, t_(s) may be computed using equation (7) for only thetransition bits. The missing t_(s) values in the repeating pattern maybe filled in using one of several possible interpolation methods. Thesimplest method is to fill in the missing t_(s) values in thecompensated edge time array with zeroes. Another simple approach is tofill in the missing t_(s) values using linear or spline interpolation,using nearby preceding and subsequent t_(s) values from actualtransitions. Then, equation (8) can be applied to get the array ofcompensated voltage values, V_(s).

There are many serial data waveforms that may not be well-represented bythe simple linearized model shown in FIG. 7, with a constant slew ratefor each high or low bit. However, the above disclosed methods may beextended to allow for multiple slew rates per bit, as shows in FIG. 8.

FIG. 8 shows two unit intervals representing the logical bit sequence [10]. Unlike FIG. 4, where each bit is modeled by a single edge slew rateand a single horizontal slew rate, each bit in FIG. 7 is modeled by anedge slew rate plus three horizontal slew rates. For example, this maybe done by dividing each unit interval into four zones of equal width,with the first zone centered on the nominal edge time and the third zonecentered at t_(ref). For the first zone, the parameters t₁ and SR_(V)are determined as discussed above. For each of the three horizontalzones, a corresponding V₁ and SR_(H) parameter may be determined usingactual samples nearest to the center of that zone, as described abovefor the simplest waveform model.

It is apparent from this that the approach discussed above can beadapted to the more complex model of FIG. 8. The most straightforwardapproach is to speculatively apply equation (7) three times, each timeusing the measured values of t₁ and V₁ with one of the mean slew ratesSR_(H1)-SR_(H3). Each of the resultant t_(s) values (which may be calledt_(s1), t_(s2) and t_(s3)) represent an estimate of the true horizontalwaveform displacement under the hypothesis that the true horizontaldisplacement caused the corresponding slew rate segment (represented bySR_(H1), SR_(H2) and SR_(H3)) to instantaneously shift to the actualvoltage measurement point t_(ref). Estimate t_(s2) is typically the mostlikely since t_(ref) falls in the center of the second horizontal zoneso it corresponds to zero jitter. If estimate t_(s2) is smaller thanhalf the width of this zone, the hypothesis that SR_(H2) was the correctslew rate to use is attractive. Estimate to should be the properestimate to use only if the instantaneous jitter that to represents isapproximately ¼ of a UI to the right (late in time, or a positive valueaccording to the proposed convention), so that slew rate SR_(H1) wouldfall at the point where V₁ was measured. If t_(s1) is calculated to benear ¼ of a UI, this hypothesis becomes attractive. Finally, thehypothesis that t_(s3) is correct is attractive if it is near −¼ of aUI, since that amount of waveform shift would cause SR_(H3) to fall atthe voltage measurement point. So the extent to which each hypothesis isconsistent with its resultant jitter estimate can be used as a selectioncriteria.

A basic assumption that led to the development of equations (7) and (8)discussed above was that the time and voltage displacement at the middleof each data edge and the time and voltage displacement at thesubsequent center-of-the-UI were the same. This is a reasonableassumption for timing jitter and voltage noise occurring at lowfrequencies. As the frequency of the jitter and noise approach asignificant percentage of the data rate, the degree of correlationbetween two points separated by ½ of a unit interval drops.

To account for this, additional processing can be done prior to theapplication of equations (7) and (8). After t₁ and V₁ are measured,low-pass filters can be applied to both, before they are used tocalculate t_(s) and V_(s) in the area where the assumptions are not met.Recall that t₁ and V₁ are calculated for every UI, as discussed above,so each of t₁ and V₁ is actually an array of values rather than a singlevalue. For example, t₁ is actually [t₁₁, t₁₂, t₁₃, . . . t_(1N)] ifthere are N unit intervals in the waveform, and it can be represented as[t₁] as a reminder that it is an array of values equally-spaced in time.It is straightforward to use digital filtering to apply a low-passfilter to this array, for example using either convolution or FFT-basedmethods. The arrays [t₁] and [V₁] may each be low-pass filtered to yieldnew arrays [t_(1LP)] and [V_(1LP)]. The individual values from the newfiltered arrays can be substituted for the corresponding values from theunfiltered arrays when equations (7) and (8) are applied.

Up to this point, one apparent-jitter array ([t₁]) and oneapparent-noise array ([V₁]) have been directly measured, and onetrue-jitter array ([t_(s)]) and one true-noise array ([V_(s)]) have beencalculated using equations (7) and (8), or variations thereof, with thegoal of more accurately decoupling the effects of jitter from noise.

Using these arrays, a two-dimensional probability density function (PDF)of uncorrelated noise may be generated and used as described in U.S.Pat. No. 7,522,661, discussed above, by using the following steps.

First, a spectrum of timing jitter is generated by performing a Fouriertransform on the array [t_(s)]. The magnitude of this spectrum is amodified periodogram power spectrum of the timing jitter. This isseparated into deterministic frequency components and random frequencycomponents by identifying frequency components that have a significantlyhigher magnitude than the local surrounding frequency spectrum. Therandom components are filtered out of the magnitude spectrum to form apower spectrum of the uncorrelated deterministic jitter.

Second, based on the deterministic frequencies determined in the firststep above, the complex spectrum generated from [t_(s)] is filtered toremove the random frequency components, and the remaining deterministicfrequency components are inverse-Fourier-transformed to create atime-domain record of the uncorrelated deterministic jitter. Thepeak-to-peak, root-mean-square (rms), or other useful values of theuncorrelated deterministic jitter can be determined directly from thisrecord.

Third, the time-domain record of the uncorrelated deterministic jitterfrom step two is converted to the form of a histogram, which can beinterpreted as the probability density function (PDF) of theuncorrelated deterministic jitter.

Fourth, steps one through three are repeated using the voltage noisearray [V_(s)] to produce a PDF of the uncorrelated deterministic noiseas well as peak-to-peak and rms values.

Fifth, a complex spectrum of timing jitter is generated by performing aFourier transform on the array [t₁]. Using the deterministic jitterfrequencies determined in step one, this spectrum is filtered to maskout those frequencies and leave only the random timing jitter. Thisspectrum is inverse-Fourier-transformed to provide a time record of theuncorrelated random jitter.

Sixth, the time record of the uncorrelated random jitter from step fiveis converted to the form of a histogram of jitter amplitude versusfrequency-of-occurrence. This histogram (which can be accumulated acrossmultiple individual captured waveforms) is plotted on a Q-scale, andlinear asymptotic fits to the left and right sides of the Q-scale plotare used to estimate the rms amplitude of Gaussian random jitter and thedual-dirac amplitude of non-Gaussian random jitter.

Seventh, the rms amplitude of Gaussian random jitter from step six isused to form a Gaussian PDF that can be extended to the left and rightalong the horizontal axis (into the Gaussian tails) to levels ofpopulation lower than present in the measured data.

Eighth, the dual-dirac amplitude of non-Gaussian random jitter is usedto form a dual-dirac PDF consisting of two spikes each with negligiblewidth but probability density of ½, separated by the calculatedamplitude value.

Ninth, steps five through eight are repeated using the voltage noisearray [V₁] to produce an estimate of the Gaussian random voltage noiseand the dual-dirac amplitude of non-Gaussian random voltage noise, andPDFs of each of these.

Tenth, the PDF of the uncorrelated deterministic jitter from step threeis convolved with the PDF of Gaussian jitter from step seven and the PDFof non-Gaussian random jitter from step eight to produce a PDF of allthe uncorrelated jitter.

Eleventh, similarly, the PDFs of uncorrelated deterministic noise,Gaussian noise and non-Gaussian noise are convolved to produce a PDF ofall uncorrelated noise.

Twelfth, the one-dimensional PDFs from steps ten and eleven are used toproduce a two-dimensional PDF of uncorrelated jitter and noise. The usesof this two-dimensional PDF to produce a BER eye contour are asdescribed in U.S. Pat. No. 7,522,661.

Having described and illustrated the principles of the disclosedtechnology in a preferred embodiment thereof, it should be apparent thatthe disclosed technology can be modified in arrangement and detailwithout departing from such principles. We claim all modifications andvariations coming within the spirit and scope of the following claims.

What is claimed is:
 1. A method for determining jitter and noise of aninput signal, comprising: acquiring at least one uncorrelated waveformrecord by an acquisition unit of the test and measurement instrument;determining a correlated waveform based on the at least one uncorrelatedwaveform; dividing the correlated waveform into unit intervals; dividingthe at least one uncorrelated waveform into unit intervals; measuring atiming displacement (t₁) between the correlated waveform and theuncorrelated waveform for each unit interval to form an apparent-jitterarray ([t₁]); measuring a voltage displacement (V₁) between thecorrelated waveform and the uncorrelated waveform for each unit intervalto form an apparent-noise array ([V₁]); calculating a horizontal shift(t_(s)) between the correlated waveform and the uncorrelated waveformfor each unit interval to form a compensated edge time array ([t_(s)]);and calculating a vertical shift (V_(s)) between the correlated waveformand the uncorrelated waveform for each unit interval to form acompensated amplitude voltage array ([V_(s)]), wherein the horizontalshift and the vertical shift are calculated for each unit interval usingthe following equations:t _(s)=(V ₁ +SR _(V) *t ₁)/(SR _(V) −SR _(H)), andV _(s) =V ₁ +SR _(H) *t _(s), wherein SR_(V) represents the slew rate ofthe uncorrelated waveform on the vertical portion of the uncorrelatedwaveform and SR_(H) represents the slew rate of the uncorrelatedwaveform on the horizontal position of the uncorrelated waveform. 2.(canceled)
 3. The method of claim 1, wherein the horizontal shift iscalculated for each transition bit unit interval and set to 0 for eachnon-transition bit unit interval.
 4. The method of claim 1, wherein thehorizontal shift is calculated for each transition bit unit intervalusing the equation for t_(s) and the horizontal shift is calculated foreach non-transition bit unit interval using nearby preceding andsubsequent unit interval horizontal shifts by interpolation.
 5. Themethod of claim 1, further comprising filtering, using a low-passfilter, the timing displacement and the voltage displacement prior tocalculating the horizontal shift and the vertical shift.
 6. The methodof claim 1, wherein the equation for t_(s) is calculated a plurality oftimes, using a plurality of slew rates, and the method further includesselecting one of the plurality of calculated t_(s) values for each unitinterval based on the resultant jitter estimate.
 7. The method of claim1, further comprising generating a two-dimensional probability densityfunction of uncorrelated noise using the apparent-jitter array, theapparent noise array, the compensated edge time array, and thecompensated amplitude voltage array.
 8. The method of claim 7, furthercomprising generating a bit error rate diagram based on the generatedtwo-dimensional probability density function.
 9. The method of claim 1,further comprising generating a bit error rate diagram based on theapparent-jitter array, the apparent-noise array, the compensated edgetime array, and the compensated amplitude voltage array.
 10. The methodof claim 1, wherein the test and measurement instrument is a real-timeoscilloscope.
 11. A test and measurement instrument, comprisingacquisition means configured to receive at least one uncorrelatedwaveform record; and processing means for: determining a correlatedwaveform based on the at least one uncorrelated waveform; dividing thecorrelated waveform into unit intervals; dividing the uncorrelatedwaveform into unit intervals; measuring a timing displacement (t₁)between the correlated waveform and the uncorrelated waveform for eachunit interval to form an apparent-jitter array ([t₁]); measuring avoltage displacement (VD between the correlated waveform and theuncorrelated waveform for each unit interval to form an apparent-noisearray ([V₁]); calculating a horizontal shift (t_(s)) between thecorrelated waveform and the uncorrelated waveform for each unit intervalto form a compensated edge time array ([t_(s)]); and calculating avertical shift (V_(s)) between the correlated waveform and theuncorrelated waveform for each unit interval to form a compensatedamplitude voltage array ([V_(s)]), wherein the horizontal shift and thevertical shift are calculated for each unit interval using the followingequations:t _(s)=(V ₁ +SR _(V) *t ₁)/(SR _(V) −SR _(H)), andV _(s) =V ₁ +SR _(H) *t _(s), wherein SR_(V) represents the slew rate ofthe uncorrelated waveform on the vertical portion of the uncorrelatedwaveform and SR_(H) represents the slew rate of the uncorrelatedwaveform on the horizontal position of the uncorrelated waveform. 12.The method of claim 11, wherein the processing means is furtherconfigured to generate a two-dimensional probability density function ofuncorrelated noise using the apparent-jitter array, the apparent noisearray, the compensated edge time array, and the compensated amplitudevoltage array.
 13. The method of claim 12, wherein the processing meansis further configured to generate a bit error rate diagram based on thegenerated two-dimensional probability density function.
 14. The methodof claim 11, wherein the processing means is configured to generate abit error rate diagram based on the apparent-jitter array, theapparent-noise array, the compensated edge time array, and thecompensated amplitude voltage array.